Wigglers and undulators are magnetic assemblies used in synchrotron radiation (SR) sources and free electron lasers (FEL's). An exploded view of a wiggler/undulator can be found in FIG. 10. The terms wiggler and undulator are used interchangeably, and in the present application the term undulator is used to refer to both. Briefly, an undulator consists of a pair of opposing magnet arrays, which create an oscillating magnetic field in the gap separating the arrays (i.e., the gap between the arrays). A high-energy electron beam passing through this gap parallel to the arrays will wiggle back and forth in its trajectory because of the periodic magnetic field. Some undulators also include poles to be coupled to the magnets, respectively. The structure and operation of an undulator are known in the art (see, for example, U.S. Pat. No. 5,010,640), and undulators are commercially available from STI Optronics of Bellevue, Wash.
Undulators are periodic magnetic structures, and their magnetic field is essentially sinusoidal. Many undulators have a fixed field direction, and these are called linearly polarized undulators. Some undulators known as elliptically polarized undulators have an adjustable field direction. Some other undulators have a magnetic field direction that rotates. These are known as helical undulators. The temperature compensation method of the present invention can be used with all types of undulators, specifically including these three types.
For a variety of mechanical and magnetic reasons, the strength and centerline of the magnetic field in the gap in an undulator can vary with temperature. This is true for both permanent magnet undulators and electromagnet undulators. In permanent magnet undulators, there is a multitude of individual magnets. The strength of these magnets can vary with temperature, which will directly impact the field strength of the undulator. For example, the strength (or flux production) of Neodymium Iron Boron (NdFeB) magnets vary by −0.1%/C.° and the strength of ceramic ferrites vary by −0.2%/C.°, both near room temperature. As linearly polarized undulators, both permanent magnet undulators and electromagnetic undulators have upper and lower assemblies. If an undulator uses steel poles, the poles will expand as the temperature increases, which will change the gap spacing between the upper and lower assemblies. The gap change causes the field strength of the undulator to vary.
Likewise, the mechanical structure that holds the entire undulator will expand or contract with temperature. This will again change the magnetic gap (between the magnet arrays), which leads to a field strength change. Further, if only a portion of the mechanical structure that holds the undulator expands as the temperature increases, this will shift (e.g., raise) the magnetic centerline.
These temperature dependencies can cause unacceptable performance variations of the FEL or SR source. When this occurs, there is a need to correct for the strength variations or the centerline shifts so as to restore the performance.
The prior methods for addressing the temperature dependencies consisted of using entirely mechanical means. For example, in one prior method, when the center of the arrays of magnets moves due to thermal expansion, a mechanical mover is used to move the entire undulator up or down to compensate for the change. This is quite difficult as undulators can weigh several tons and be several meters long. In addition, many applications require micron level control of the movement, so the apparatus usually needs high accuracy and precision. Yet, the motors and electronics required to achieve high accuracy and precision can be exposed to high radiation levels in the undulator's operating environment, and this radiation can easily cause failure of the motors and/or electronics. Radiation resistant equipment can be very expensive and complex, and not always available.
In another prior method, a mechanical structure that holds the undulator is made of specially chosen but dissimilar materials. This is done so that the relative rates of thermal expansion among the dissimilar materials would correct for the temperature effects. In one example, when the temperature increases, the magnetic strength decreases, so the mechanical apparatus is designed to decrease the mechanical spacing between the two assemblies (halves) of the undulator as the temperature increases. This increases the magnetic field at the gap between the two assemblies to compensate for the reduction in the magnet strength. The prior method used titanium, aluminum, and steel. Titanium is very expensive, difficult to machine, and has mechanical creep over time. In addition, since the differences in the thermal expansion coefficients for the different materials are large, there are many induced stresses in the mechanical structure. These lead to deformations, lack of predictability, stiction, twist, warp, and other mechanical problems. Engineering solutions to these problems are challenging and do not always work. This means that there can still be residual field strength and centerline shifts that will need to be corrected. In short, this prior method is complex, expensive, hard to engineer, and furthermore, has no means of correcting for design deficiencies. Either this approach would work, or the entire design would need to be changed and iterated to make it work, and yet this process may not converge due to the inherent complexity of the approach.